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Textbook Page

Questions

358

2, 3, 4, 5

361

12, 14, 16, 17, 20

362

21. 28, 29, 30

363

31, 32, 33, 34, 35

Solutions

2. The risks of deaths of individual policyholders are largely independent, and therefore are

diversifiable. Therefore, the insurance company is satisfied to charge a premium that

reflects actuarial probabilities of death, without an additional risk premium. In contrast,

flood damage is not independent across policyholders. If my coastal home floods in a

storm, there is a greater chance that my neighbor's will too. Because flood risk is not

diversifiable, the insurance company may not be satisfied to charge a premium that reflects

only the expected value of payouts.

3. The actual returns on the Snake Oil fund exhibit considerable variation around the

regression line. This indicates that the fund is subject to diversifiable risk: it is not well

diversified. The variation in the fund's returns is influenced by more than just market-wide

events.

4. Investors would buy shares of firms with high degrees of diversifiable risk, and earn high-

risk premiums. However, by holding these shares in diversified portfolios, they would not

necessarily bear a high degree of portfolio risk. This would represent a profit opportunity,

however. As investors seek these shares, we would expect their prices to rise, and the

expected rate of return to investors buying at these higher prices to fall. This process would

continue until the reward for bearing diversifiable risk dissipated.

5. a. Required return = rf + (rm – rf) = 4% + .6 (11% – 4%) = 8.2%

With an IRR of 14%, the project is attractive.

b. If beta = 1.6, required return increases to:

4% + 1.6 (11% – 4%) = 15.2%

which is greater than the project IRR. You should now reject the project.

c. Given its IRR, the project is attractive when its risk and therefore its required return

are low. At a higher risk level, the IRR is no longer higher than the expected return on

comparable risk assets available elsewhere in the capital market.

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12. Figure follows below.

Cost of capital = risk-free rate + beta × market risk premium

Since the risk-free rate is 4% and the market risk premium is 7%, we can write the cost of

capital as:

Cost of capital = 4% + beta × 7%

Cost of capital (from CAPM)

Beta = 10% + beta × 8%

.75 4% + .75 7% = 9.25%

1.75 4% + 1.75 7% = 16.25%

beta

r

1.0

4%

11%

7% = market risk

premium

SML

0

The cost of capital of each project is calculated using the above CAPM formula. Thus, for

Project P, its cost of capital is: 4% + 1.0 × 7% = 11%.

If the cost of capital is greater than IRR, then the NPV is negative. If the cost of capital

equals the IRR, then the NPV is zero. Otherwise, if the cost of capital is less than the IRR,

the NPV is positive.

Project

Beta

Cost of capital

IRR

NPV

P

1.0

11.0%

11%

0

Q

0.0

4.0

6

+

R

2.0

18.0

17

S

0.4

6.8

7

+

T

1.6

15.2

16

+

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